cp's OEIS Frontend

A381894 Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same sum.

%I A381894 #15 Mar 21 2025 17:10:57
%S A381894 1,2,2,1,1,3,5,2,2,2,3,3,3,3,3,4,4,5,5,6,6,3,3,3,6,6,6,7,7,7,8,8,8,9,
%T A381894 9,9,4,4,4,4,5,5,5,5,6,6,6,6,6,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,11,
%U A381894 11,11,13,13,13,15,15,15,8,8,8,8,8,8,9,9,9,9,9,9
%N A381894 Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same sum.
%H A381894 Neal Gersh Tolunsky, <a href="/A381894/b381894.txt">Table of n, a(n) for n = 1..10000</a>
%e A381894 a(6) = 3 because the 4th run must have length a(4) = 1, and the potential runs 1 and 2 have the same sum as a run already in the sequence (namely 1 and 1,1). So a(6) = 3 since no run has appeared with a sum of 3 thus far.
%Y A381894 Cf. A331910, A382028, A000002.
%K A381894 nonn
%O A381894 1,2
%A A381894 _Neal Gersh Tolunsky_, Mar 09 2025